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Relation between differential polynomials of certain complex linear differential equations and meromorphic functions of finite order. (English) Zbl 1171.34060
The authors study a special second order linear differential equation with coefficients of exponential type and investigate the growth of the exponent of convergence of the distinct zeros of a differential polynomial of the meromorphic solution \(f\) of the form \(d_2f''+ d_1f' + d_0f - \varphi\), where \(f\) has a finite exponent of convergence of poles, \(\varphi\) is a meromorphic function of finite order and \(d_j\) (\(j=0, 1, 2\)) are polynomials.
34M10 Oscillation, growth of solutions to ordinary differential equations in the complex domain
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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